


A Mathematician’s Apology

by pear_tree



Category: The Last Samurai - Helen Dewitt
Genre: Academia, Future Fic, Gen, Post-Canon
Language: English
Status: Completed
Published: 2019-12-23
Updated: 2019-12-23
Packaged: 2021-02-26 00:57:16
Rating: Not Rated
Warnings: No Archive Warnings Apply
Chapters: 3
Words: 20,449
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/21829498
Author URL: https://archiveofourown.org/users/pear_tree/pseuds/pear_tree
Summary: Ultimately, Cambridge had rejected me, and of course you couldn’t apply to both Cambridge and Oxford in the same year, and Harvard had accepted me. So I went to Harvard, and that was that.
Comments: 12
Kudos: 18
Collections: Yuletide 2019





	1. In which our young hero goes up to Harvard

**Author's Note:**

  * For [yasaman](https://archiveofourown.org/users/yasaman/gifts).

> Content warning: discussion of suicidal ideation at a canon-typical level. Please see the notes at the end for more detailed (and potentially spoilery) content notes if you'd like.
> 
> I finished this novel after signups ended, saw your futurefic prompt, and felt compelled to write a treat (which turned out a bit longer than I'd expected). Happy Yuletide!

Ultimately, Cambridge had rejected me, and of course you couldn’t apply to both Cambridge and Oxford in the same year, and Harvard had accepted me. So I went to Harvard, and that was that.

* * *

A week after Kenzo Yamamoto and I made our deal, Michael from Bermondsey Boys Junior Judo said his mother wanted to invite me and all the Year 6 boys to their house for a play date. What on earth is a play date? Sibylla said. I took the train there, arrived late, and discovered everyone huddled around Michael’s computer, which was endowed with a dial-up internet connection.

Watch this, Michael said, and opened a program called Napster, which displayed a list of rock albums and progress bars. He clicked on one of them. He said: It takes a few minutes. My mum said there’s no reason for us to get the fastest internet connection. Wait, let me show you some songs I already downloaded.

He opened a folder and clicked on Oasis’s Stand By Me, and the opening guitar riff sounded through tinny computer speakers. Someone said: I heard that on the radio! Someone else said: Does it have Wonderwall?

I said: Can you upload songs?

I returned to Yamamoto the next day. A tape recorder I’d found in the house was now in my backpack. Yamamoto was playing Mozart’s _Twelve Variations on Ah vous dirai-je, Maman_ as I approached the house, and I stood outside and waited. Of course the tune was just Twinkle Twinkle Little Star, but the way he played some of the variations made you feel as though Twinkle Twinkle Little Star were the only song that had ever existed and would ever exist, and the way he played others made you forget you’d ever heard Twinkle Twinkle Little Star in your entire life. When he finished I went in. I said: I have a different idea.

I explained Napster. I said that a CD could only be an hour long and had to be split into tracks that anyone could play in any order, but that’s not at all what the concerts had been like. The whole point was that everything you heard depended on what you’d heard before, and an ordinary CD would completely undermine that.

Yamamoto picked out the first few notes of Straight No Chaser on the piano. He said: How would we make any money from this?

I said: Well, we can’t. But it won’t cost us any money to make, either, and you’re not getting paid to not give concerts and not make CDs. And it solves the problem of how to find the ten people in the world who would listen, even if you don’t go through your agent or your record label.

But who would record it?

I took the tape recorder out of my backpack. Yamamoto laughed. He played the theme of Ah vous dirai-je, Maman with his left hand. Easy as A B C.

You’d better get a lot of tapes, he said.

Yamamoto asked me to come back in a month. When I returned, I expected drums and water glasses, but there was nothing in the room except the piano. He told me he’d done all he could with the drums and with repetition per se. A following of copycats had spawned in the last few years. Young pianists would tamely reprise one piece they’d played before the interval after the interval and coyly refer to Yamamoto in their concert programmes, and young composers would write 20-minute pieces for piano with drums and tape recording and cite Yamamoto as an influence next to Terry Riley. Reporters would continue to compare his last Royal Festival Hall performance to playing a CD track on repeat. It was enough to make one despair.

I set up the tape recorder. On the first day Yamamoto took out the _Well-Tempered Clavier_ Books I and II and started playing through the pieces in an order I didn’t understand. Sometimes he’d transpose a prelude to a new key that was neither the original key nor that of the fugue that followed. He played some portions as though they were the organ preludes transcribed by Busoni and some portions as if they were the St Matthew Passion premiered by Mendelssohn’s choral society and some portions as though they were the Cello Suites committed to vinyl for the first time by Casals. Eventually I think he covered the entire set exactly once.

When we took a break for lunch, I asked him about the transpositions. He said he wanted to avoid abrupt key changes which would only produce cheap thrills that were utterly beside the point. He said that since equal temperament had destroyed the key-colours of the tempered keyboard in Bach’s time where B-flat major was cheerful and C-sharp minor was penitential and so on, one may as well take advantage of the possibilities offered by modern tuning.

I said What if you played Schoenberg’s 12-tone pieces on a well-tempered piano? and Yamamoto rolled his eyes. I said Glenn Gould thought the preludes had no musical value and Yamamoto said Yes, I know, but that’s patently ridiculous.

So it continued for two weeks. He played the Goldberg Variations and the Diabelli Variations and then he improvisationally swapped the theme of one into the structure of the other and vice versa. He played the Preludes of Chopin and Rachmaninoff and Scriabin and interspersed them with the fugues from the WTC. He played Rzewski’s _The People United Will Never Be Defeated!_ He played the Mozart and he played the Alkan. He played some pieces from memory that I didn’t recognise. When he did play from a score, I sat by his side and turned pages for him.

Yamamoto instructed me to produce a single audio file with no internal distinctions between pieces or days. I bought some patch cables from RadioShack and digitised the tapes and ended up having to split the 22-hour-long file into 30-minute chunks, since Napster limited my file size to 10 MB, but I added a README file stating that the track splits were arbitrary and represented no actual boundaries within the sound. Then I uploaded it.

At first there were a dozen downloads per day, although most of the downloaders ended up cancelling and not reseeding. I realised they’d probably mistaken this recording for one of his earlier CDs or perhaps a bootleg or a computer virus.

I played the tapes for Sibylla. She pursed her lips throughout the Prelude in C major, which sounded as though it could have been played by Mozart at age 4. Then the Prelude in B-flat started, but transposed to G major, and she said What is this? Then the Fugue in G major, which sounded how Liszt might have sounded in his prime on his tour of the Continent. Sibylla whispered What IS this? It took her two days to listen to all the tapes and then she put them on again. I wondered if anyone in the world aside from me, Sibylla, and Kenzo Yamamoto had listened to them in their entirety.

She said Yamamoto is probably the fiftieth pianist to put Rachmaninoff’s Preludes and Chopin’s Preludes on the same album, but nobody’s made it sound like THIS. And every pianist who thinks they are so very clever says well what are the Preludes the preludes to? But they’re the preludes to the fugues! And obviously I don’t mean that in the banal sense of Chopin having written the preludes with that intention in mind— She went on like this. Then she said, So this is why you’ve been playing all the Bach!

Yamamoto had loaned me his scores for the WTC Books I and II, and I had been trying to learn some preludes, the fugues being too difficult. Once you’d heard Chopin’s Prelude in C minor played immediately before the WTC Book I Fugue in C minor, though, you could really start to understand the potential in the prelude form. I thought I was onto something with my playing.

Sibylla said that my renditions in their glacial slowness had their own integrity and that perhaps Yamamoto could make another recording of Bach as though it were played by an intelligent but not prodigious 11-year-old. She was on her fifth time through the tapes when she said this.

* * *

When I arrived at my room in my first-year dorm at Harvard, two people who I assumed were my roommate and his mother were already inside, unpacking translucent bins of clothes. My roommate introduced himself as Drew and I introduced myself as Ludo. His mother said: Pluto? Oh, Ludo! I’m sorry, it’s been a long car ride from Connecticut so we’re both a little frazzled. Lots of traffic!

She was wearing a Harvard sweatshirt. She said So, Ludo, where are you from? Somewhere in the UK, I’m guessing! I told her. Drew asked what I was concentrating in and I said mathematics, maybe physics. His mother said: Good for you! I’ve never had a head for numbers at all.

Drew said he would probably concentrate in econ or government. His mother said: My older son was an econ concentrator too. But Drew’s always been a little more right-brained, so it’ll be good to have you as his roommate when he’s taking math classes. Isn’t that right, Drew? You’re taking calculus this semester?

Drew nodded and smiled and started unpacking more clothes. I looked around the room. A Harvard flag, fresh and creased from its gift shop packaging, hung on the wall. A small ceramic Virgin Mary stood benevolently atop Drew’s bookshelf and a few brand-new textbooks sat on the shelves.

I opened my suitcase, which mostly contained a jumble of clothes and some books: The Tale of Genji (which I was reading) in a set of small Japanese paperbacks, a few Schaum’s Outlines in case I wanted them for reference, _The Solid State_ whose later chapters I thought I might try reading again after a month or so of quantum mechanics. I stuffed the clothes into the dresser, and then I took the books and organised them on my new bookshelf, half-listening to the conversation on the other side of the room. Drew’s mother was asking him which freshman seminar he’d enrol in when I turned to leave. She said: It was so nice to meet you. I’m so sorry, what did you say your name was again?

* * *

About a year and a half after we recorded the tapes, someone who wrote for the _Sunday Times_ received a tip from a friend who’d read an intriguing post on a Usenet newsgroup. The original poster claimed that the suspiciously large Yamamoto recording he or she had downloaded on Napster was not a previous record or a bootleg or a virus, but something else entirely. Subsequent posters had managed to identify piecemeal what pieces were being played and at what time, though the results had been rather confusing.

Earlier that year Metallica had sued Napster, so there was an aura of illicit glamour surrounding the whole thing. People who posted on Usenet newsgroups dedicated to classical music tended not to have many opportunities to acquire that type of aura. When the _Sunday Times_ announced a ‘new’ Yamamoto recording and hinted at the difficulties involved in acquiring it, intense interest was aroused. The friend downloaded Napster and started burning the ‘record’ onto sets of about a dozen physical CDs and charging acquaintances £20 to cover costs. A few people from the newsgroup emailed Yamamoto to ask if it was really him or to argue with his interpretative choices or to tell him that the recording had changed their lives.

Yamamoto’s agent contacted him and asked to resume the relationship. What the record label wanted was to release the tapes properly.

It seemed like a logical idea. After all, the continued existence of Napster seemed more legally precarious by the day. Yamamoto got a substantial advance and negotiated a cut for the recording technician and page turner. After a lot of back-and-forth, the tapes were released under the name _Yamamoto Unfiltered: The Authentic Bootleg Sessions_. It was a 2-CD set where they split what they kept into individual tracks and rearranged almost everything into its ‘proper’ order.

Sales were moderately high, but undercut by file-sharing software (Limewire having grown in popularity). Critics said it was disjointed and incoherent.

Yamamoto was disgusted. I shouldn’t have allowed this, he said. It’s blood money. I don’t blame you, but I was thinking I’d like to give you all the royalties. At least I know a few people listened to it and that ought to be enough.

This was not exactly an enticing proposal, but on the other hand I didn’t have much of a choice. I had recently started helping Sib with her typing so that we could break even every month and neither of us were happy about it. The first time I did it she’d been furious, and I’d said What if I’m genuinely interested in the tips in _Modern Landscaper_ and just wanted to digitise them for posterity as soon as possible? Then you can’t possibly object on any rational grounds. Really, the only way you could disincentivise me from doing this in the future is to delete the work I’ve done but I don’t think you’ll do it.

I had this response prepared because I knew Sibylla would be angry. She didn’t say anything for a while and then she said Well I’m trying to remember what it was that Cicero supposedly wrote to his son although that’s the only surviving fragment so who can say. You are the only one out of all persons in the world whom I would wish to excel me in all things. Solus es omnium a quo me in omnibus vinci velim. I said Cicero the Younger was a mediocrity and didn’t excel his father in anything except possibly his military record but of course being dissatisfied with one’s offspring is something you and Cicero Sr have in common. Then Sibylla looked for a moment like she was trying to not crack a smile, but only for a moment.

I knew she would be angry but it had to be done. Sibylla didn’t object after that.

I ended up convincing Yamamoto to split the royalties 50/50. With the royalty payments, Sibylla could work 10–20 hours a week and we’d still have a bit of money left over, and we’d still have a cushion from the advance in case she didn’t want to type at all for a week. 10–20 hours is what Sibylla was averaging on her own, anyway, but now she didn’t have to feel as bad about it. She was not doing much with the remaining 148–158 hours of the week aside from the usual.

Originally I’d dreamt too big. I’d secretly asked after vacant houses in our neighbourhood, but I’d underestimated how high the rent would be for houses that most people would find acceptable to live in. In any case, at age 13 I could not legally rent a house in secret, furnish it, and induce Sibylla to move after the fact, which was the only way it would have worked out anyway.

I got as far as hiring someone to replace our windows and fix the heat. The house was poorly insulated, but it would be better than nothing. It was already October and I could not bear another winter of riding the Circle Line and watching Sibylla huddling in her coat under the fluorescent lights. I never sold the silk heart; it sat on the same shelf as the tapes.

* * *

On the first day of class, I went to the first meeting of Expository Writing: Bioethics in the Twenty-first Century. The person sitting next to me asked if she could borrow a pen. I’d gone to University Stationery the previous day and spent $28.92 of my scholarship money on a 10-pack of Staedtler 0.1mm pens and a few Rhodia notebooks (unruled, of course), and now I loaned her one of the pens.

We all introduced ourselves. She was Cindy Wu, from New York City, concentrating in mathematics. I was Ludo Newman (Cluedo? No, Ludo, short for Ludovic, it’s kind of a middle name. Oh, I see: Newman, Stephen), from London, concentrating in mathematics or maybe physics. We continued around the room: economics, English, government, econ or gov or maybe both, econ with a minor in statistics, psychology, not sure yet, biology, neuroscience, not sure yet but maybe econ.

After class Cindy caught up with me and said: What kind of math are you interested in?

I said: Well, I’m interested in Fourier transforms—

Cindy said: So, functional analysis, then?

I said: What—

Cindy said: Sorry, I was just curious. I don’t know a lot of other math people here. What dorm are you in?

I said: Hollis. What kind of maths are _you_ interested in? And what’s functional analysis?

She said: Oh, great, I’m in Matthews. I think those are close by, right? I did all sorts of things in high school but I think what I really want to do is algebraic geometry.

We started walking back to our dorms together. She said: Anyway, functional analysis is—you know how a Fourier transform is just a linear operator on the space of functions? Well, in general, you can study linear operators on any infinite-dimensional vector space with a topology. People used to just think of Fourier transforms as a way to solve differential equations but the field’s come a long way since then.

I did _not_ know that a Fourier transform was just a linear operator on something something something or that the field had come a long way, but I nodded anyway. Of course I was embarrassed to not know, but that itself was embarrassing; after all, there was no shame in ignorance but in the refusal to learn. Still, I didn’t want her to know how ignorant I was, so I changed the subject and asked her about her mathematical background.

Cindy said: Well, it’s not that interesting.

Cindy had grown up in Flushing, and every weekday she’d taken the train for an hour to Bronx Science, and then for another hour to Columbia to take math classes. Over the summers, under the auspices of a gifted students’ program, she’d coauthored two papers in number theory with a professor there. Her parents also both happened to be professors of mathematics at Queens College. That wasn’t as helpful as one would expect, she said.

I was rattled but tried to not show it. It was likely that most of my classmates had not published two mathematics papers before entering college, and I happened to be talking with one who had. Limited conclusions could be drawn from small sample sizes. When we reached the Hollis entrance, Cindy said: Well, I don’t want to keep you, but it was nice to meet you! Let me know if you want to study together at some point.

I said that would be nice, and I waved goodbye.

Cindy was much nicer than, say, Sorabji. Granted, I hadn’t done anything like tell her I was her son and then that I was not her son, so it was too early to tell. Still, I selfishly hoped that not every first interaction with another mathematics concentrator would be like this, given that there were an average of around 40 mathematics concentrators each year and I did not want my ego bruised 40 times. I went back into my dorm.

* * *

I had written in my university applications that I was homeschooled. I had also written Sibylla’s reference letter for me. We’d argued about it, where I’d said that out of the two of us she was the only one with a proven track record when it came to writing reference letters for university & she had said that it was simply the more rational option for me to do it myself. Ultimately I’d given in.

My Harvard interviewer was a middle-aged Barclays investment banker with an American accent. He had concentrated in mathematics, had gone to Wall Street afterwards, had worked 70-hour weeks, had undervalued importance of family & authentic human connection, was now making up for lost time, was now giving back to community by interviewing next generation of Harvard students (which, incidentally, kept him a little younger).

You’re 15! he said, smiling warmly and conspiratorially at me. So I guess it’s true after all, that mathematics is a young man’s game.

I smiled knowingly at him so he’d know I’d understood the reference. I also happened to remember that in the same book G. H. Hardy had written the following:

> It is very hard to find an instance of a first-rate mathematician who has abandoned mathematics and attained first-rate distinction in any other field. […] Every young mathematician of real talent whom I have known has been faithful to mathematics, and not from lack of ambition but from abundance of it; they have all recognised that there, if anywhere, lay the road to a life of any distinction.

My interviewer said, So, Stephen, why do you want to concentrate in math? and I gave him a Hardyesque answer about the joy of creativity in pure mathematics. I did not give him an answer about having been pressed up against a pane of glass for years, trying to read mathematical texts but not understanding them and settling instead for books about people doing mathematics. Case in point: _A Mathematician’s Apology_, which was not a very good book. It contained a great number of assertions, one being that ‘real’ mathematics was useless for war, subfields such as aerodynamics being ‘repulsively ugly and intolerably dull’ and not ‘real’ mathematics (if only Hardy could have lived to see his beloved field of number theory put to use in military cryptography!). You couldn’t even trust mathematicians to refrain from committing these kinds of simple logical mistakes.

My interviewer asked me what I did aside from math. Take it from me, Stephen, don’t work too hard! Life is shorter than you think. I remembered that the Harvard interview guide had said to be specific and enthusiastic about my passions outside the classroom. I told him about the Kenzo Yamamoto CD and didn’t mention the fact that, while he didn’t blame me, he had disavowed the album that had resulted from our collaboration.

My interviewer became wistful. He discoursed on the importance of the arts. He said that he might take his daughters to Wigmore Hall to see a concert one of these days. The oldest one was nearly in college, she was quite a talented violinist, maybe it would be a time to connect. He wrote something in his notebook with a fountain pen.

Cambridge hadn’t bothered giving me an interview.

Anyway, Sibylla was still a U.S. citizen, so I qualified for financial aid and got a full scholarship to Harvard. The timing was excellent because Sib had just been made redundant at her job by a piece of optical character recognition software. We were scraping by on CD royalties and taking slivers of our library to Skoob, but obviously what would have made things easier is Sibylla not having to buy food for both of us.

For my fifteenth birthday I’d received a second-hand adult-sized bicycle, since I’d grown several centimetres in the past year, and a brief lecture on the horror of traumatic head injury resulting in brain damage along with an addendum that of course I could rationally evaluate risks for myself. I spent the summer learning how to ride in traffic instead of on the pavement. Mostly it was a matter of training myself to make split-second decisions even when afraid.

Finally, in late August, I packed a suitcase and got on a plane to Boston.

* * *

Aside from Expos, I was taking Quantum Mechanics I, Honors Abstract Algebra a.k.a. Math 55, and Foundations of Tonal Music. I had applied for approval to take more than 4 classes—had had my application rejected by the Resident Dean—had been informed this rule & other rules were in place to facilitate freshman success—had found myself being advised by advisor on importance of balancing academics with making connections with peers especially when living independently from parents for first time. Even so, I sometimes dropped in on Sentence Structure and Intermediate Indo-European.

Paul Dirac’s _The Principles of Quantum Mechanics_ had been published in 1930 and soon eclipsed every other monograph on quantum mechanics available. Einstein had liked to bring the book on holiday to read for pleasure. When Dirac taught courses at Cambridge, his lectures had been identical in content to his book, on the grounds that he’d already formulated the most logical way of presenting the material. What point would there be in deviating from that? If a student asked a clarifying question, he would repeat exactly what he’d already said.

His students hated his class or else they adored it. Chandrasekhar, who won the Nobel in ’83, took the course four times and said the course was a piece of music you wanted to hear again and again. Had Dirac been right? Had he discovered in 1930 the optimal way of presenting quantum mechanics to ambitious undergraduates? I’d gotten _The Principles of Quantum Mechanics_ from the Harvard library, and I liked to imagine Dirac speaking crisply and carefully to his lecture hall containing not a few future Nobel Laureates, Fellows of the Royal Society, and so on. Dirac had invented bra-ket notation and introduced it to the world in his book: a quantum mechanical state was |ψ⟩, a ‘ket’, or its mirror image ⟨ψ|, a ‘bra’. The inner product of two states ⟨ψ| and |φ⟩—something like their similarity—was represented by sticking the two of them together to form a bra-ket ⟨ψ|φ⟩. Their _outer_ product was |φ⟩⟨ψ|, inelegantly called by some a ket-bra.

A mathematician might dully write the same objects as v and v*, but bras and kets were much more expressive. An inner product always resulted in a tidy package of a scalar ⟨ψ|φ⟩ and an outer product always resulted in a squarish jumble of an operator |φ⟩⟨ψ|. It was easy to go for a long time without thinking much about mathematical notation, but when I read _Principles_ I sensed for the first time that specialised notation could be a kind of language unto itself, that it could be a means of communication you actually wanted to use.

Anyway, in Quantum Mechanics we weren’t using that book, but rather _Principles of Quantum Mechanics_ by Shankar and _Modern Quantum Mechanics_ by Sakurai. They weren’t bad and the professor wasn’t bad, but I found it difficult to imagine either author filling up a lecture hall by simply reading from their books and difficult to imagine an interesting book resulting from the lectures I’d been hearing. You couldn’t win them all.

* * *

Cindy and I started studying together. We had a standing appointment in the Cabot Science Library every Tuesday afternoon, when neither of us had classes or seminars or colloquia to attend. Cindy was taking commutative algebra and algebraic topology so she could join the graduate students in algebraic geometry next year & I was learning about groups for the first time.

In the first week Cindy had seen me reading as usual and said You’re just going to READ that book?

I hadn’t understand what she meant, and she’d had to explain that you can’t read a mathematical text like a novel or an instruction manual or even something in a new language. If you saw a Lemma, Theorem, or Corollary, you should try to prove it for yourself, and then you should try to think of counterexamples and figure out why they were never counterexamples after all. If you saw a Definition, you should play around with examples both inside and outside the definition in order to understand why the definition was worthwhile in the first place. Math books were written backwards in that mathematicians spent all their time groping in the dark for interesting objects, and having stumbled upon one would present it to you in the form of Definition 1.1.1 as though God himself had spoken it. What you had to do was to trace the steps backwards. If you did this enough then at some point you might be able to take your own steps in the dark.

I figured I could start with Definition 2.3.17 since I’d gotten that far before reaching the limitations of reading parts over and over until they made sense. Cindy asked me for a sketch of the proof of the normal subgroup theorem (Theorem 1.6.2) and I tried to remember what the book had said and she said that this wasn’t like memorising The Odyssey In Latin Or Whatever and that maybe I should just start from the beginning with Definition 1.1.1 for a group. A group had four axioms: closure, associativity, identity, inverse….

Progress was slow. I hoped she was right.

I’d also met some other mathematics concentrators, some in my Math 55 class, some at the first Undergraduate Mathematics Association social of the year, where people had mostly arrived and talked to each other in pre-established clumps while eating supermarket cake. Nobody else I met had mentioned publishing any papers. Cindy hadn’t gone, and I asked her why not afterwards.

She said: Oh, the socials? Don’t remind me. It’s all these people who knew each other from high school math competitions and won’t stop talking about them. I don’t want to deal with it.

She said: We have so much math to do.

That last part was something she said a lot and it would brook no argument. We always did have a lot of math to do, so I didn’t press the topic further.

* * *

I didn’t see much of my roommate. He played a CD titled Mozart for Study and Relaxation while he studied; he went running in the mornings while I slept; he said a rosary every night; his mother called him once a week. I hadn’t brought any sheets or blankets with me, intending to buy some at a vague future date, and Drew had seen me sleeping on the mattress and asked if I wanted to borrow any bedding since his mother had insisted on bringing extras of everything. He never brought it up again, so I hoped I could keep using his indefinitely.

I entered my room one day to retrieve Shankar and Sakurai, and found him listening to an opera recording. A silvery soprano sang I love you so! How could you leave me? in Italian while the orchestra swelled grotesquely. I said: I had no idea you liked opera. Which one is this?

Drew said: Oh, I don’t actually really know anything about opera. I’m just listening to this on a suggestion from a friend. He told me the soprano was his favourite.

He grabbed the jewel case. It’s _Alcina_ by Handel. I don’t really remember the plot, I think this is the evil sorceress. She’s singing about her former lover who just escaped from her enchanted island with the help of his fiancée who’s disguised as her own brother, but I think the sorceress’s sister is also in love with the quote unquote brother. Something like that. Are you an opera person?

I said: Unfortunately, I’m not. Sibylla—I mean, my mother refused to let any Italian opera recordings into the house unless you count Mozart and she never bothered to remember the names of any of the singers. I think she liked _Moses und Aron_ and I don’t know what else.

Drew laughed. He said: I don’t know what that is. Yeah, my mom used to put me in a jacket and tie and drive us down to the city occasionally to see the opera. She had a weird hang-up about going to the opera alone and my dad never wanted to do it. I never really understood what was going on onstage and I don’t think she did either, but she had a friend on the board or something who she wanted to impress.

I said: Huh. To be fair, I’ve never seen a staged opera, so I wouldn’t want to dismiss the medium unfairly. It’s as though I’d only heard plays but not seen them. Not to imply, of course, that people who can’t see can’t enjoy the theatre, but the point is that there are other dimensions.

Drew said: I hadn’t thought of it that way.

I looked at the jewel case. Joan Sutherland’s name and photo were on the front. The music shifted into a stormy B section and Joan Sutherland’s voice turned dark and imperious. I’m the queen! Either he returns to me or he suffers and dies! Drew said: Well, for what it’s worth, the friend I borrowed this from told me to not care too much about the plot and just focus on the singing. He also said—well, he said a lot of other things about opera and Joan Sutherland but that was the gist of it.

The music returned to the A section. The orchestra resumed its droning repeated figures. I love you so! How could you leave me? The music was perfectly awful but you could listen to Joan Sutherland gliding on the high notes forever, as long as you didn’t think too much about what she was saying. I said as much to Drew, and he smiled and said Maybe I’ll tell my friend you said that.

* * *

There had been a paper due on the ethics of stem cell research. Walking back from the library at 2 a.m., I saw two people sitting on a bench in the Yard. I couldn’t see who they were, but I heard one of them say, And this was during rehearsal! I recognised him from his voice—he was in my Foundations of Tonal Music section, and I thought his name might have been Thomas. The second person laughed and said, Wait, seriously? And I realised it was Drew.

They were holding hands when I passed by. I smiled and waved.

Drew came back to our room half an hour after I did.

He said: It’s not a secret around here, but please don’t mention anything to my mom when she visits for parents’ weekend. I don’t know when I’ll tell her but it’s not going to be now.

I said of course, really it’s barbaric that you have to keep this from your mother but I understand. Drew smiled. Barbaric! he said, in my accent. I’m not sure I’d go that far.

The ceramic Blessed Virgin gazed down at us in benign condescension. I brushed my teeth and Drew said a rosary and we went to sleep.

* * *

I called Sibylla. She told me she’d been hired again by her previous employer, not to type but to fix mistakes made by the OCR software. The capabilities of the software had been vastly oversold: like an incompetent palaeographer it had a tendency to read rn as m, and c as e, and of course the whole set i l I 1 ! and to some extent t were hopeless, so modern might become rnodem and modernisation might become rnodemisatlon, and that would be on a good day and only if there was no italicised text. The company kept renewing the rather expensive contract because nobody wanted to admit that a rather expensive mistake had been made. They’d originally hired someone else, but that person turned out to be about as reliable as Sibylla in turnaround time whilst making more errors.

Sibylla said: Well, it’s not so much worse than typing.

I said: Surely if you’re willing to essentially change jobs then you should also be willing to consider other jobs. Deleting m and replacing it with rn or vice versa a thousand times a day can’t possibly be the ideal job even given your constraints.

Of course I hoped that Sib would listen, but saying this was like trying to stop a train by throwing a fistful of sand at it. Sib said that she would not subject herself to interviews where someone with a clipboard deigned to ask her what are your greatest strengths and weaknesses and please provide some examples of when you have been a team player. This was at least an answer to the question, so I didn’t press further.

I told her I was taking Quantum Mechanics I and Math 55 and Expository Writing: Bioethics in the Twenty-first Century and Foundations of Tonal Music and occasionally dropping by Sentence Structure and Intermediate Indo-European. She asked what we were covering in Intermediate Indo-European and I told her. She mentioned she’d been dipping into _Ptolemaic Alexandria_ again.

Drew happened to be in our room. When I hung up he looked at me, and for a moment I was afraid he would smile or even crack a joke: Moms, right? But of course he didn’t.

* * *

After the call, I met my Math 55 classmates to work on the problem set. Things went smoothly until someone asked me: So, how do you know Cindy Wu?

I said that we met in Expos. More people turned to listen. Someone else said: Wait, you didn’t do math competitions in high school? Do you not have those in England? I said I didn’t know.

Someone said: Cindy is that girl who won three gold medals in a row at the International Math Olympiad, right? Someone else said: Yeah, she’s on the Harvard Putnam team but she won’t talk to the rest of us. I’ve barely ever seen her. Someone else said: Wait, isn’t she a sophomore? I’ve never actually seen her in person.

I said: What are you talking about?

Someone else said: Cindy was pretty much legendary in high school, I’m from Palo Alto and even I know who she is. I heard she crushed everyone at competitions and she wrote five number theory papers with some Columbia professor. How come she’s friends with you?

I liked to think that I was more magnanimous to my fellow mathematics concentrator than Cindy, but I was starting to see what she meant. I felt irrationally protective & I was slightly on edge from my phone conversation earlier that day. I said: I have no idea how to answer that question. Maybe she just wants to be left alone.

Someone said: Okay, that’s fair. Someone else said: Isn’t she taking algebraic geometry? I guess she’s just too good for us. I said: We have so much math to do. Would you mind terribly if we got back to Problem 5.3?

* * *

A few days later, I happened to look more closely at Drew’s bookshelf. Next to the introductory calculus and introductory economics textbooks was Augustine’s _Confessions_ in the Loeb two-volume edition.

I hadn’t read Augustine, since it wasn’t the sort of thing Sibylla kept in the house. I picked up Volume I and started reading, mostly from the Latin side, although the English crib helped. My Latin was getting rusty. There were notes pencilled in the margin, some theological and some grammatical.

I didn’t have time to put it back before Drew unlocked the door and entered. I apologized. He said no, it’s totally fine. Do you want to borrow it?

I said sure, thank you. Did you read this in high school?

Not in high school. Did I ever tell you? I actually went to a two-year liberal arts college in Montana before I came here, it was one of those Western canon kinds of places. By the way, that English translation isn’t the best, it’s just the Latin edition I had to get. I can recommend a better one if you want.

No, that’s all right, I read Latin.

Oh, nice! I didn’t know that. You’re pretty lucky, I didn’t get to start taking Latin until I got to St. Catherine’s.

He quoted something about arriving in Carthage and being surrounded by some unholy something or other; I couldn’t quite make it out through his ecclesiastical pronunciation. Then he said: I just love Augustine. He’s so evocative, you know? I should read this again before I forget all my Latin.

I said I didn’t know, I hadn’t read Augustine. He said: Sorry, I didn’t mean to be annoying about it. It’s the zeal of the convert, I guess. I promise I’m not actually pushy.

It turned out that Drew, from a family of Christmas-and-Easter Presbyterians, had crossed the Tiber in his first year at St. Catherine’s, which promised a classical liberal arts education while being thoroughly Catholic in all but official designation. In high school he’d declared a desire to go off the beaten path, with one brother having graduated from Harvard and another from Yale, and his parents had only consented upon seeing St. Catherine’s statistics for graduates continuing their education at the Ivies. He’d read Augustine in his first semester in Foundations of Western Civilization I, and, somewhat against the odds for a boy from suburban Connecticut whose only form of physical exertion had been track and field, had learned how to ride a horse and shoot a rifle, in that still, cold Montana landscape with no one but him and his few dozen classmates and professors and God for miles around.

He said: I didn’t have an intense emotional experience or anything. What people don’t get is that it was more of a rational, intellectual thing. I read all those books and I started believing that the Church is who she says she is, you know?

Against my instincts, I nodded. Drew’s sincerity was not in doubt, but you could tell when he was talking like himself and when he was echoing something he’d heard from a professor. I tried not to hold this against him. He went on.

The parish church was in the nearest town, and the Catholic students would go on the bus on Sundays and holy days of obligation, the girls in their lace mantillas. The following semester, around the time Drew was reading Milton in Western Civ II, he’d been received into the Church along with two of his classmates at the Easter Vigil.

The bus had stopped running by the time it ended, and he and his classmates had broken their fast with bacon and eggs at the 24-hour diner, along with a bottle of champagne someone had snuck in. It was an early Easter that year, freezing cold by the time they left the diner, and the stars were so bright.

Sancta Maria, stella maris, ora pro nobis.

Drew’s parents were tolerant at first. Perhaps Drew could become a public Catholic intellectual and write for the _National Review_! Then Drew had declared a desire to discern whether he had a monastic vocation, and suddenly their son’s newfound papism was no longer so tolerable. The oldest brother was working for an Ohio senator, handpicked from a pool of promising D.C. interns, and the second-oldest was a rising star at Bain working on something abroad that he couldn’t tell his parents about. They both had bright futures ahead of them, and Drew had shown just as much academic promise; it would be a pity to squander it.

His mother had said: All we’re asking is that you get your Harvard degree. You can still become a monk after that! We just don’t want you to close off your options so early.

He said to me: Honestly, I don’t think I was actually called to monastic life, it was more like I didn’t want to leave Montana and get back into the real world. Sorry, I know that was a lot of talking, usually people aren’t really interested. It’s just that— I spent the summer after my first year there at a Benedictine monastery in Oregon, so it was middle of nowhere in Montana then middle of nowhere in Oregon then back to Montana, and then I had to come back to the suburbs. I guess it doesn’t feel like I’m really back or I wasn’t ready for it or something. Sometimes in the mornings when I get up I still expect to hear bells.

There had been other impulsive choices, like an ill-advised fling with an Anglican boy who was now reading classics at Oxford. Drew said: I hope he’s enjoying Oxford more than I’m enjoying Harvard. I think he always kind of wanted to be a _Brideshead Revisited_ character like the guy, what’s his name, it’s been a while since I tried to read it and I never finished it so I didn’t even know the other guy Charles converts at the end until later. Anyway, you never asked about the gay thing, that’s usually the first thing people mention.

I said: Oscar Wilde was gay and Catholic and his plays were brilliant and people loved him.

Drew said: I read that he converted on his deathbed. It’s not so hard if you only have to be both for a few hours. Sorry, I didn’t mean to sound bitter about it, since I’m not, really, although people don’t usually believe that either. One thing is that I guess most people either become Catholic first or become gay first, and I did both at around the same time, which was— I really don’t recommend that, by the way, especially not at a college where a quarter of the class has gotten engaged to each other by the time they graduate. Don’t get me wrong, it wasn’t that bad, but—I mean, not that it was a great place to be if you weren’t straight, I’m not saying

He said: Well, I thought at the time like maybe it would be a relief once I’d left, but— I don’t know. I thought maybe coming _here_ would be a relief, but

Drew rubbed his face. He said: Well, Thomas—my, well, you saw him—we actually met at mass at St. Paul’s and he’s been Catholic for his whole life, so maybe that’s the right order to do things in. Or maybe Oscar Wilde had the right idea, who knows.

I said: I see. Well, I’ll keep that in mind. If I discern a calling to being either gay or Catholic then I shall thoroughly pursue one before taking any steps in the other.

Drew said: Right, exactly. Also, now that you bring it up, Thomas is actually going to be in The Importance of Being Earnest this semester, I don’t know anything about it but I heard it’s good. You can come if you want, I’m sure he’d like that.

* * *

November arrived. It was now cold enough that it was hard to be outside. I’d bought a second-hand bicycle from a campus listserv, and I’d been trying to get out of campus on the weekends, but it was difficult to find time. Some nights I climbed to the roof of my dorm building or other buildings nearby. It hadn’t been difficult to figure out which buildings had unlocked doors to the roof and which ones had doors that would open after a bit of work.

I had a view of the Yard but it wasn’t a particularly good view. When the weather turned cold and dry, the campus became an unbeautiful sickly grey, and the New England collegiate autumn with its bright red brick buildings and leafy oak trees was already long gone. The thing was, when you were at Harvard, it was easy to forget that any other place existed. I needed to get outside of it or above it, in a purely spatial sense, or else I’d sink in too deep and never get out.

When I was much younger, I’d been under the misapprehension that Sib had dropped out of Oxford because of me. The timing had roughly lined up, and what other reason could she have? When I mentioned this in passing once, at around age 8 or 9, she’d become quite upset and told me in no uncertain terms that it wasn’t true and she didn’t want me to think so. I didn’t have a good sense of her reasons, then or now, even having read her private notes years ago—how could Roemer have been worse than _Carpworld_?—but I had a sense of unease about being here, and my reasons didn’t have to be her reasons.

I liked mathematics, which after all was the point. I liked Cindy, I liked my roommate, I liked plenty of people. But I feared I was being suffocated by something I’d been left unprepared for by my first 15 years of existence and which was difficult to name. Symptomatic were the paperwork and the bevy of advisors and counsellors and having to carry my Harvard ID to go anywhere and needing Sibylla’s signature on everything (easily forgeable, and she’d be bored if I bothered to ask her, but it was the principle of the matter), but it wasn’t really any of those things. The real question was this: How did everyone already know what they were going to do? Even when you spoke with someone who claimed not to, it would become clear that what they meant was that they’d thought about doing 2 or 3 different types of jobs and hated the idea of all of them. The world you were in at Harvard had a way of being both all-encompassing and terribly small.

I’d cycled to Walden Pond last week and made some loops around the pond and saw Thoreau’s cabin. On the way there I had been thinking some embarrassingly mawkish half-formed thoughts about art and solitude and so on, but seeing the cabin itself cured me of that, and on the way back I was completely preoccupied with the details of actually surviving there. Thoreau had received assistance from his friends, but suppose he hadn’t? How much wood would he have needed for the winter? If he hadn’t been vegetarian, which animals would have been the most worthwhile to trap and hunt? By the time I reentered campus I’d calculated that it probably wasn’t possible unless you wanted to spend many weeks chopping wood and doing little else, which I did not, so that was out of the question. But surely there were countless other possibilities waiting.

* * *

I started tutoring Drew. He said that the problem with a Great Books approach to maths was that you spent a year reading Euclid and learning how to do things like inscribing a regular pentadecagon in a circle when everyone else was learning useful things like calculus. I tried to reassure him by saying that Newton’s _Principia_, contrary to most people’s expectations, didn’t use what we consider to be calculus at all and that it was largely geometry, but this didn’t cheer him up much.

I’d started with the idea that when you taught something to someone, you had to start building a new layer of knowledge only when the previous layer had been built, but of course you could only understand the logic of the progression if you already knew all the material. If you were a complete novice, then you’d ask questions that cut through all the layers of complexity with no regard for whatever order the material was supposed to have been presented in. (If someone asked you why the sky was blue, could you answer that in any _meaningful_ way without saying something about how Rayleigh scattering worked?) Whenever Drew asked a question, I found myself having to slice the layer cake differently each time to produce a sensible answer.

I’d have done it for less, but Drew insisted on $50 per hour, so after a few weeks of tutoring I was pretty flush with cash. I bought a winter coat and a pair of snow boots from Goodwill and some CDs from Cheapo Records (most of which I’d already listened to, but Sib wouldn’t part with hers) and a big pile of books from the MIT Press Bookstore during the sale where they put the good stuff on their loading dock and let everyone have at it. I sent the book about modernist architecture to Sib in the mail since it was her birthday soon.

I now had more books than could fit in my suitcase even if I’d put nothing else in it, but with my income I could probably buy another suitcase.

Mathematical concepts had a way of feeling more tangible over time, and the most familiar ideas felt like multifaceted crystals I could almost hold and turn over in my hand. I thought I’d known all that was interesting to know about single-variable calculus, but having to say words in order to generate the same concepts in someone else’s mind meant that you had to keep turning the crystalline structure again and again, and gradually you gained more facility in turning, and occasionally you’d see it from an angle you’d never seen before. I’d been learning so many things without having to teach them to anyone else. What had I been missing out on? I wondered, naturally, whether Sibylla had ever derived any purely selfish pleasure from explaining Greek grammar to me and placing her books and highlighters into my hands, and I hoped the answer was yes.


	2. Speaking of ill-defined questions

Cindy asked me what I was doing for Thanksgiving & I said I had no plans and didn’t really know what the holiday was. She said, Wait, didn’t you say your mom was American? I said it wasn’t her kind of thing.

Cindy knew little about Sibylla and everyone else I knew at university knew less. From Cindy’s point of view, she was an expat with a classics degree from Oxford and had raised and homeschooled me and did part-time work for a publishing company. Describing Sibylla like this seemed to be lying by omission, somehow, but it was hard to know what else to say.

Cindy said: Well, you’re welcome to spend Thanksgiving with my parents in New York and eat Chinese food if you want. Honestly, your mom can even come if she wants, since we have a guest room _and_ a pullout bed.

I didn’t say anything. Cindy said: No pressure, though! Think about it.

I said thank you and that I’d think about it. It might have been rude to say immediately that Sibylla wouldn’t come, although she wouldn’t. I would probably just go without her. I’d never been to New York City before, and the truth (which Sibylla would find revolting) was that I badly wanted to hail a yellow cab & order from a hot dog stand & take the express train uptown & so on. But it would be untruthful to proceed without at least asking.

I called Sibylla the next day. I said: My friend Cindy asked if you’d like to come to New York City for Thanksgiving dinner.

Sib said: Thanksgiving dinner! I suppose they’ll have a turkey and yams with marshmallows and _cranberry sauce_. You haven’t known horror until you’ve seen a cylindrical mass of cranberry sauce squelch and wobble its way out of its can, bearing the mark of the corrugations imprinted on its surface.

It would have been sensible to give up here. The most likely outcome would be that we’d keep circling around until I didn’t want to go to New York anymore either. But I realised, suddenly, that I wanted her to come. That wasn’t at all sensible, but I figured I could stall for time while I thought it through. I said: Actually, I think they’ll have Chinese food. Do you want to come?

Sib said: Why, that’s even _more_ American in a way. You know, last year I saw a set of Christmas decorations in a Chinese grocery store where Santa Claus and his reindeer were depicted exactly like the wonderfully pink, cherubic children one sees on Chinese New Year paper wall hangings and it was perfect, the _reindeer_ had chubby rosy cheeks, you could call it kitsch but somehow it transcended the label entirely.

I had enough money saved up from tutoring and there was nothing else I needed to buy. Perhaps I could earmark a bit of it in case any interesting books came along later. I thought fast. I said: Do you want to come? I have $521, which is more than enough for a round-trip ticket provided we buy tickets immediately. Any travel agent would agree that prices are going up now and there’s no time to lose.

Sib said: How did you get $521? You haven’t _actually_ been engaging in insider trading, have you? I’ve no moral objection to it, as you know, but it’s legally risky and I hope you’re ready to incur those risks.

Sib had recently said after having read an article about some wealthy American cooking show hostess that to criminalise insider trading was to penalise knowledge and that a truly free market ought to reward the knowledgeable instead of the merely fortunate, and I’d said that if I were on trial I’d advance that argument in the hope of jury nullification. I said: No, I’ve been tutoring my roommate in calculus. By the way, Cindy’s parents are both mathematics professors at Queens College.

The worst outcome was that Sibylla would come and she’d hate Cindy and her parents and make it obvious, causing me to lose my closest friend at university. I thought that perhaps I shouldn’t bother. Sib said: Your roommate needs help with calculus? That’s very kind of you, but I hope for his sake that he’s not reading mathematics.

Perhaps I could warn Cindy in advance. But about what, exactly? It was also true that the trip would only be for a few days. If we made a poor impression on Cindy’s parents then maybe Cindy would still forgive me. In any case, there would be no good reason for us to stop studying together. I said: No, he’s concentrating in economics. You’ve never been to New York before, have you? You could go to the Met or the Getty or the Whitney. You could go to Bauman Rare Books.

Sib said: Well, the Getty is in Los Angeles. Then she was silent.

I could tell she was actually considering it and would likely do it. I was shocked but didn’t show it. Any sign of having anticipated her decision would potentially spoil it.

The obvious fact occurred to me that Sibylla was—or, at least, had been at one point—the kind of person who would sleep with someone before being rude to them. Perhaps I was worrying excessively. I said: Well, I was thinking of buying the tickets at noon Eastern Time tomorrow before the price goes up further. I’m going to Tonal Music now, but I’ll buy them then if I don’t hear anything from you in the meantime.

Sib said: I suppose Chinese food is a more appealing prospect than a desiccated turkey cooked with spite. Well, I’ll consider it.

I smiled. We said goodbye.

I called the travel agent at noon the next day. The tickets cost $504, so I was cutting it a bit close.

* * *

On our way back from Expos, I told Cindy that Sibylla and I both wanted to come to New York. She said: I can’t wait to meet your mom! She seems like she’d be really interesting. Much more so than my parents.

I shrugged. Some sort of conversation would eventually have to be had, but everything I learned about changing the subject I learned from my mother. I said: But your parents are maths professors. Don’t you talk to them about maths all the time? What’s that like? How did they become professors, anyway?

Cindy said: Well, honestly, we don’t talk about math at home. It’s not like I ever needed them to help me with my homework, you know?

She didn’t seem to have much else to say. Then she said: But yeah, sure, I guess I can tell you how they became professors. It’s not that interesting.

* * *

Dr. Wu had gotten his doctorate at sunny Stanford beginning at age 22 and ending at age 27, after a Houston upbringing and an undergraduate stint at UT Austin. Dr. Huang had gotten hers at Beida, beginning at age 18 and ending at age 27, with a five-year interlude during which she’d mostly dug irrigation ditches and repaired farm equipment. Her original doctoral advisor never returned after the interlude, and she never saw him again.

The new advisor, as one would expect, was more deft at pulling strings than the old. He had contacts in the United States and somehow managed to get a visa for her. The political difficulties had been enormous, and part of the case made by her advisor was that their work in combinatorics, their own and that of their colleagues’ in the States, in enumerating a kind of abstruse mathematical object that required a monograph to explain, was utterly, thoroughly, unfathomably useless; no amount of collaboration could possibly cause a security threat to either country.

In the end, the newly minted Dr. Huang had arrived in Indiana, having learned English mostly from the tattered English-Chinese mathematical dictionary that had once belonged to her first advisor, well-prepared for lunchtime chats with her new colleagues as long as they confined themselves to mathematical topics. She and her future husband had nearly crossed paths many times; in fact, they’d both won gold medals at the International Mathematics Olympiad within a few years of each other, on opposite sides of the Cold War playing out in miniature among high-school-aged children. Eventually they’d both ended up as postdocs at Columbia, though they hadn’t met that way. That had required a chance encounter at a bus stop between Dr. Wu’s visiting parents and Dr. Huang, the former being on the lookout for nice marriageable women everywhere they went.

When Cindy started to tell people this story, they usually said, Did your parents have an academic rivalry where the sparks flew between them? Were they colleagues who then became something more? And she’d have to explain, no, my mom studies combinatorics and my dad studies partial differential equations, so they had literally no reason to talk to each other.

Cindy said: Anyway, it’s not like they ever pressured me to do math. My brother is—ugh, don’t even get me started on him.

I hadn’t known Cindy had a brother. We had reached the Matthews entrance, and we went on to her suite. She continued: People assume that my parents must be putting a lot of pressure on us, but it’s not like that. I know how this sounds, but I always did fine in high school and they left me alone. My friends used to complain about their Asian parents and I had to pretend to commiserate. I know, that must be so hard, right? What a sob story. Anyway, my brother. He got into Stuy, but he gets straight Bs and spends all his time playing Ultima Online, and my parents don’t care.

We reached her room in her suite. Everywhere there were sheets of white printer paper with math written on them in coloured gel pen. We sat down on her bed. Cindy said: My dad was one of those people who cruised through his entire academic career—not that he was the smartest, but he never ran into any serious obstacles and was never obsessive. When I mentioned the Putnam was coming up, he said that in his freshman year he forgot the date and went out the night before and didn’t show up for the exam until after lunch. I guess if you’re the one Chinese guy in your frat in Texas then you have to overcompensate somehow. And my mom has this idea that she didn’t work this hard to make it here as a math professor only for her daughter to also slave away to be a math professor, you know? Don’t get me wrong, they’re supportive, but they’re not extremely enthusiastic or anything.

Also, I said my brother’s always playing Ultima Online, but he doesn’t even actually play the game! He just writes bots and exploits and then sells them to people for in-game currency. It’s not even real money! I always asked him why he doesn’t just hoard his bots and exploits so that he doesn’t cause inflation through other people using them, which presumably makes his own in-game money less valuable, but he always had some complicated in-game economic reason for why it still provided positive utility for him that I never understood. And he’s not applying to any good schools next year. My dad’s always like, I went to a state school, and your mom went to a _state_ school, ha! Don’t be such an elitist, Cindy.

Anyway, that’s not even the point. The point is that maybe I just want to do as much math as I can. Is there anything really wrong with that? But they don’t seem to like it for some reason.

I didn’t understand this at all. Changing the subject had worked well in a way, but maybe all roads led to the same place. I said: You know, when I was 11 I thought about applying to university but Sibylla said I should wait until I was 16. I shaved a year off that, but otherwise I think she was right.

Cindy flopped back onto the bed. She said: 11!! We’re so OLD! I can feel all this time passing that we’ll never get back. When I was 11 I did an assignment in middle school saying that studying any subject other than math was pointless because everything that you can’t say in mathematical notation is ill-defined and therefore illogical.

I laughed. Cindy said: I know you’ll hate me for this, but I still believe it a little bit. I promise I’ll read the Odyssey, I still have the copy you bought for me on my bookshelf, I just haven’t had time to start it yet.

I said: Sure, maybe after you retire and finally get your professor emeritus title. I’m sure it’ll happen at age 40 after you’ve successfully compressed a lifetime’s worth of work into two decades. Do you think you’d still want to be a math professor if your parents hadn’t been math professors?

Cindy said: Speaking of ill-defined questions. Seriously, though, if my parents were different then of course I’d be different so it would be a different ‘I’ and the comparison becomes meaningless. Presumably I just want to be a math professor for the same reasons that you do or anyone else does.

I said: Well, I’m not sure I do, actually.

For a few moments Cindy had the look of someone trying and failing to assimilate new information, which was rare for her. She said: What are you going to do after grad school? Please don’t tell me you’re going to work at a hedge fund. You know at the career fair when they tell you that financial mathematics is full of interesting unsolved problems that it’s all bullshit, there’s a reason why they have to pay you so much to do it.

I figured there was no point in saying that I might not even go to grad school. I said: I don’t know. I thought I could maybe travel to Siberia.

Cindy said: You’re not kidding, are you.

I said: Someone told me you won three gold medals at the IMO. Is that true?

Cindy grabbed a pillow, put it over her face, and yelled something into it. Then she flung it aside and said: I only won two. It’s not a big deal, my mom did it too. Did you hear that from some freshman?

I said: Why don’t you like any of the other math concentrators? As far as I can tell, most of them are nice, smart, and interesting, or at least they’ve got two out of three which isn’t bad.

Cindy said: It’s just a difference in perspective. I just want to move forward and actually learn things without anyone pointlessly dwelling on the past and that’s all anyone is ever obsessed with.

Everything I knew about trying to stay on topic I also learned from my mother. I said: That’s not true. There are a few of them who do talk about high school nonstop, but that’s about half of all the first-years here. If you think it’s bad for us then you should see any of the econ events, not that I’ve been to any but my roommate complains about them all the time. Why don’t you actually want to talk to anyone?

Cindy didn’t say anything for a few seconds. I was afraid we’d be at a permanent impasse; I could see it now, lasting years and years and years until one of us died.

Then she said: I didn’t want to tell you this, but I actually started at Harvard last year and had to leave.

Why?

Another silence.

I just couldn’t do it for some reason. When I got here I couldn’t do any of the work that was in front of me. It was like everything in my brain had been taken out and replaced with static. I don’t know how to explain this but it’s true, you can’t imagine something like that but when it happens to you it’s the worst thing in the world. My parents managed to negotiate with the administration and I took an Incomplete in all my classes and left sometime in November. But now I’m back and everyone I knew is a sophomore, and I can’t stand all the new freshmen or anyone I knew before and I don’t want to talk to them.

I said, What’s different this time?

I don’t _know_, Cindy said. I don’t know why it happened. Of course my parents said I was burnt out and needed to rest, because that’s just how they are, but I didn’t feel like I was burnt out or tired, I just didn’t feel like anything. I’d just sit down and try to do math and nothing would come out. I went to a psychiatrist and she said maybe it was seasonal depression and then she asked me about ‘cultural factors’, like my parents were pressuring me or worse, and I never got her to understand what I was trying to say.

Anyway, I’m back now, and nothing’s really different. So clearly it’s not seasonal and it’s not cultural factors, and I just—I don’t have anything to blame it on, you know? So it seems like it could come back at any time, and I won’t be able to do anything about it. I managed to redo this year and so far I’m doing fine, but I can’t just keep doing that forever. I mean, you can’t just keep redoing years of your career and pretending the previous one never happened. What if I’d been a postdoc?

I said: I’m so relieved you told me. Cindy said: What? I said: Sorry. I just—I was worried you’d just refuse to tell me forever and I’d have to keep guessing.

Cindy laughed. She said: I guess it’s good to actually say it. Obviously a lot of people here know, but I hate the idea of them knowing. The thing is that all the serious math concentrators know each other and we all know academia is like climbing a mountain without a harness where if you make one wrong move you fall off and die. I’m not sure anyone would be mean about it, but—I mean, they’d be _nice_ about it, which is even worse.

Right, I said.

What could I say? I couldn’t say that a bad year or two wasn’t the worst thing, considering. I certainly couldn’t say that it was fine if it happened again. If someone told you that something was the worst thing in the world, it would obviously be at best insufficient to assert that it was fine.

Yeah, I figured you’d get it, Cindy said. In fact, I should have known you’d be low-key about it. I don’t even know what I was worried about. Well, now you know.

I flopped onto the bed next to her. I said: So that’s why you wanted to be friends so early on. Because I didn’t know you and had never heard of you.

Cindy said: Well, at first, yes. But that’s not the only reason anymore.

I said: So you’re still not going to talk to anyone.

Cindy put the pillow over her face again. Then she set it aside. She said: Okay okay okay, I understand what you’re getting at. But it doesn’t change how annoying— Look, we can’t all be as friendly as you are.

I sat up. I said: Just come to a seminar reception with me instead of leaving right away. It won’t kill you. You can even just eat snacks if you want, the mini-muffins after the topology seminar on Thursday are especially good. Most of the people are grad students and they’re too preoccupied with their own problems.

Cindy looked at her ceiling for a few seconds. Well, all right, she said. I’ll go.

* * *

I returned to my dorm room. Thomas was there and Drew wasn’t. He said: Oh, hi again, Ludo! Drew’s at the convenience store picking up snacks, but he’ll be back in a moment.

Thomas and I would sometimes talk before or after Tonal Music. I knew he was planning to concentrate in English, that he was especially interested in the literature of the early twentieth century, that he’d considered auditioning for the Gilbert and Sullivan Society but didn’t think he was a strong enough singer for any of the good roles. I asked him how the play rehearsals were going and he asked me how the math was going. He said: I couldn’t help but see your CD collection. Do you ever listen to anything but the great solemn piano works performed by the great pianists of the twentieth century? Drew mentioned that your mother forbade you from listening to Italian opera lest it corrupt your ears and I just think that’s hilarious. Nothing against your mother, of course, I’m sure she’s wonderful.

I said I liked Joan Sutherland in _Alcina_. He laughed and said, You don’t have to say that. But I’m glad I’ve gotten Drew to listen to some opera. The thing is that people think the text of an opera is its _score_, so they think that an opera is something for musicologists to look at and analyse in their heads and whatever it is that the singers are doing is just a consequence of the text, but that’s just completely silly not to mention anachronistic if you think about it, of course it’s all about this Romantic conception of the discrete artistic work. Of course in that light the plots make no sense and the music is trivial and slapdash or it’s a masterpiece and the composer is a genius. The truth is that the text of an opera is an individual _performance_ and it’s always primarily been about the divas and the costumes and the camp and the ephemeral thrills of the human voice. Anyway, I don’t mean to bore you.

Thomas could talk very quickly when he had a lot to say. He said: The point being, _Alcina_ is nobody’s idea of a foundational work of Western civilization but sometimes you just have to loosen up a little.

I said: Did you also attend a Catholic college? And Thomas crossed himself in jest and said, Of course not. I’m happy for Drew that he came home to Mother Church there but I’d never go to a place like that. Everyone comes out of those places stoically masculine and convinced that Catholicism is all about the pure light of reason. Drew’s still got the bends and we’ve got to decompress him. Did he give you the runaround about how his conversion was purely rational? I bet he did.

I nodded. He said: We’ve probably got a few minutes. Don’t tell him I told you this, but it has to be done, I can’t stand the idea of people thinking the Church is all about syllogisms. You know that little statue of Mary on the bookshelf? Drew’s ex gave him that. I don’t know if he mentioned that to you, but his ex—I mean, I have nothing against Anglicans [he gestured at me], but this guy was a real piece of work. He was one of the ones who thought we were all superstitious and hysterical and that only the English knew anything about restraint and good taste. When he found out Drew was thinking about converting he bought what he thought was the tackiest Mary statue at the Catholic shop in town and gave it to him as a joke. I’ll elide the details here, but at a very very bad time Drew found herself praying to her and he said he knew she was listening, he just _knew_, and that was what compelled him. It wasn’t really because he read Augustine or Thomas Aquinas or whatever he told you, although I suppose that probably did something too, you know, primary and secondary causes and all that. So that’s why he still has that chintzy little statue and won’t get rid of it.

I said: First of all, I’m Jewish, so you needn’t worry. Or, rather, my mother is, or rather her mother is. Naturally I don’t have a horse in this race, but your account of it seems more honest at least. I just finished the _Confessions_ and I certainly haven’t converted and I’d like to think I’m not immune to logic.

I said: Also, Augustine says he converts because he hears the voice telling him Tolle lege, tolle lege, take it up and read, it’s explicitly treated as a sign or a miracle and not a matter of pure reason. He’s not exactly a Christian Bertrand Russell is what I’m saying.

Oh, let’s not speak of Bertrand Russell, Thomas said. Also, Don’t tell anyone this either, but I never finished the _Confessions_. I tried to read it a few years ago but I found it terribly boring.

I said: Your secret’s safe with me.

Thomas said: Really, the problem is that Drew’s afraid that if people know he’s gay they won’t take him seriously as a Catholic, which is why he’s got to be so _rational_ about it all the time so people will know he’s serious. If you like the incense and the bells and the weeping too much then you’re a gay stereotype, and we can’t have that, can we? He’s not self-hating in the usual sense. It’s just a peculiar combination of circumstances—

The door opened. Drew said: Oh, hey, Ludo, I didn’t know you were here.

I said: We were just talking about the _Confessions_. Drew said: Oh, so you finished it! What did you think? You can tell me, I won’t be offended if you didn’t like it.

* * *

On the day before Thanksgiving Cindy and I boarded a Fung Wah bus to New York. Cindy had taken the trip plenty of times before, so she let me take the window seat and took out a book to read. Sibylla would be arriving later that night.

I looked out the window and watched Boston slip backwards behind me, then the endless trees on the side of the road, the deciduous trees dark and nearly leafless. The sky was grey. Signs for rest stops, fast food restaurants, small towns passed by. I imagined that all along the freeway, people would be leaving motels they’d checked into the previous night, getting back into their cars, driving away.

The truth was that I’d applied to Cambridge and Harvard, but also Princeton, Columbia, MIT, the University of Chicago, the University of Michigan, Stanford, and UC Berkeley. I didn’t know which American universities had strong mathematics departments, so I played it safe by picking all the almae matres of past American Fields Medalists. I didn’t apply to any other universities in England or anywhere else. When the acceptance and rejection letters had started to come in, I had rushed to the mailbox every day to collect the letters and hide them. I don’t think Sibylla would have said anything if she’d seen, but I didn’t want her to know. All I needed was for one university to accept me and not charge me too much (which was to say, any) money to attend, and the rest didn’t matter.

It wasn’t that I wanted to find Sibylla’s parents. I imagined saying to some old bitter couple who owned a motel somewhere: I’m your grandson! The idea was intolerable. It was difficult to even imagine Sib’s parents being old; I pictured them eternally in a room with dingy wood paneling and a mahogany upright piano, her mother smoking and scowling and her father pacing up and down. I couldn’t imagine teenaged Sibylla in the scene either, but of course I was seeing it through her eyes.

I didn’t entirely know what I’d come to the States for. One answer was that I’d come to study mathematics, and I was doing exactly that. But I realised I’d been hoping that both being across the ocean from Sibylla and being where she came from would help me understand her, somehow, as though simply being here would unstick something and I’d finally be able to say and do the right things. Of course it hadn’t. For one thing, going to Harvard brought you no closer to the world of dingy one-story motels off the interstate, which was of course part of the point of places like Harvard in the first place. I didn’t even know what the desired kind of ‘understanding’ would entail, or how I’d know if I’d understood, or how having an understanding would actually help. I didn’t know what I was looking for.

The view of I-90 can’t possibly be that interesting, Cindy said.

What? I said. Oh, I was just thinking about something. What are you reading?

Cindy was, to my surprise, reading a book in French. I didn’t know you read French, I said, and Cindy said, Well, not really. I took it in high school so I know all the connecting words, and then the nouns are pretty easy to figure out since they’re all math words, obviously homomorphismes are homomorphisms and so on. Anyway, it’s the first volume of _Éléments de géométrie algébrique_. Do you know what that is?

I didn’t. Cindy said that it was Alexander Grothendieck’s magnum opus. She said, Algebraic geometry is—well, at a very basic level, think of a set of zeroes of a multivariate polynomial. (What came to mind was a memory of Sibylla teaching me to graph polynomials: x+1, x2+1, x3+1. Of course I’d learned some maths before that, and some after, but the moment when you first saw an algebraic object in your mind take wobbly geometric shape on paper, drawn by you with a pen too thick for your hand, wasn’t easily forgotten.) I said okay, I’m thinking.

Cindy said, So, in general, these are complicated curves in any number of dimensions, and algebraic geometry was originally about using algebraic techniques to solve geometric problems about these objects. She said that new approaches had been found by twentieth-century mathematicians, and Grothendieck had been the greatest of them. Instead of solving specific problems he had built abstractions on abstractions on abstractions. He had wanted to build a theory so general that more specific results would easily emerge from the generality. When asked to explain his work, he’d spoken of not using a hammer and chisel to crack open a nut but submerging it in water until it softened and yielded. He’d spoken of a sea that imperceptibly, inexorably rose until it covered the earth.

Cindy said: I’m surprised you’d never heard of him before. Part of the reason he’s so notorious is that he cut all his institutional ties ten years ago and went off to live alone by himself.

Why? I said.

Cindy said: I’m not sure if anyone knows. He quit the IHÉS because he didn’t want to be funded by the military, and I think he refused to come to the United States because he couldn’t in good conscience check the box where he promised to not overthrow the government, if that gives you some idea of what he was like. He still sends huge manuscripts to his collaborators but he’s not publishing anymore.

And nobody knows where he is? I said.

Yeah, Cindy said. Well, not to state the obvious, but he’s probably somewhere in France. Why, are you going to go find him? I don’t think he really wants to be found.

Right, I said.

Cindy said: Well, anyway, I’m just reading this over the holiday as a break from my other work. I figured it’d be fun to see how far I could get.

I looked over her shoulder. She was only on Chapitre 0, Préliminaires, but my being able to read French did not really help. Eventually I dozed off, and when I woke up the bus was inching through Lower Manhattan.

* * *

We disembarked in Chinatown. New York was busy and noisy in a way that I liked immediately—it was clear that you could walk anywhere, take the train anywhere, or read a book for a few hours anywhere and fit into the city without anyone noticing. We took the 4 to Grand Central (at which point Cindy let us go upstairs to see the Beaux-Arts interior) and then the 7 to Flushing, and then we walked to Cindy’s parents’ apartment.

Cindy’s parents were at work. Kevin was home; fantasy battle sounds emanated from his room. Cindy yelled Hey Kevin, we’re home! to no response. She got a huge bag of frozen dumplings from the freezer and cooked them all on the stovetop and we ate them with black vinegar.

There was a baby grand in the living room and a shelf full of non-mathematical books. The only signs of mathematical life that I could see were a few issues of the _Notices of the American Mathematical Society_ on the coffee table (two of each issue, one addressed to each of her parents) next to a stack of _New Yorker_s. Obviously, I realised, the mathematics books would be in her parents’ offices.

I was also stunned to see an issue of _The Hobbyist Carpenter_, which Sibylla had typed up at some point, addressed to Dr. Wu. Cindy said What are you looking at? I said It’s nothing, and Cindy said Oh, yeah, I know, my dad’s kind of a dweeb. He got really into building furniture like he’s a suburban dad with a garage or something, but he has to do it all at the shop at the college. Typical midlife crisis for a math professor who’s never worked with his hands before. Hopefully that’ll be me in twenty-five years. He did build this coffee table, though, so that’s cool.

I slipped the _The Hobbyist Carpenter_ under the _New Yorker_s when Cindy had her back turned.

It was noon. I wanted to see the city, but I wanted to save anything that Sibylla might want to see for Friday, so we went to the Transit Museum. We looked at the old train cars and subway tokens and played with a model of the mechanical signal system. I tried to not worry about Sib arriving, disliking her surroundings, being miserable.

When we got back on the train, Cindy said: Huh, it feels weird to be on a normal train with a normal MetroCard again. Then she said: Did you not like the museum?

I said: No, I did.

Cindy frowned. I couldn’t evade the topic forever. I said: I’m worried about Sibylla’s arrival.

Cindy said: You mean about her flight? To be honest, Ludo, I think airline travel is pretty safe. Maybe you should just try to take your mind off it.

I shook my head. I thought about what to say. I said: No, I’m worried about what happens when she gets here. Sibylla is—she’s not great around new people, or really people in general.

Cindy said: Well, my parents can deal with my brother just fine. Sorry, I’m kidding. What do you mean?

I said: Oh, don’t get me wrong, Sibylla can be excruciatingly polite when called for. I think it’s unlikely she’ll be a poor guest, although in all fairness I’ve never personally witnessed her in a similar situation so it’s hard to be certain.

Cindy said: Okay. So what are you worried about, then?

I didn’t know how to say I was worried she’d just be incredibly unhappy. What kind of a thing was that to worry about? I said: I’m worried she won’t like it. She basically never travels. She hasn’t been back to the States since she left for Oxford so it’s been two decades and I don’t know how she’ll take it.

Oh, I hadn’t realised that, Cindy said. Well, worst comes to worst, it’s only for two days and she can stay in the guest bedroom the whole time if she really hates it.

I guess you’re right, I said. I didn’t try to sound convinced but Cindy didn’t say anything further.

We rode the train for a while. Cindy said: Also, by the way, what should I call your mom?

You should call her Sibylla. Definitely not Ms. Newman or anything like that.

Okay.

* * *

We had dinner back at the apartment. Dr. Wu was an affable backslapping sort of guy and Dr. Huang was more sardonic. I’d still been half-expecting them to grill me on maths, but they mostly asked me about how our trip had been and how I liked the States and what we planned to do in the city and so on. I was nervous and couldn’t eat much.

Sibylla arrived at around 10 p.m. Hearing her footsteps on the stairs filled me with anticipation and dread, but she opened the door and of course it was just her. She was polite and gracious and Cindy’s parents commiserated with her about having to fly through Newark, and then Sib said I’m sorry but I’m afraid I’m extremely jet lagged and Dr. Wu said Well, we shouldn’t keep you up any longer! and Dr. Huang said Yes, please make yourself comfortable.

It was surreal to see Sibylla in this completely normal Chinese-American household in New York City. She didn’t seem unhappy or bored when she retreated to the guest bedroom. I wished I knew.

Cindy got some mugs and turned the electric kettle on. We started setting up the pull-out bed. She said: Are you still worried?

No, I said. Well, yes.

I don’t understand what you’re worried about. That seemed fine to me.

If Sib hates this trip, it’s my fault.

Why? Technically it’d be my fault for inviting her, if that makes you feel better.

The kettle started whistling. Cindy made us hot cocoa from a mix and added marshmallows and said: You know, there’s really no reason to ever get the kind with the chalky little marshmallows when you can just add your own instead.

My mug said Combinatorics Summer School ’99 and hers said Houston Astros. We sat on the sofa bed and watched an X-Files rerun. You should try to get some sleep, Cindy said afterward.

* * *

The next morning I woke up, worked on my problem sets, and then went to take a shower. When I entered the dining room I saw Sibylla and Cindy sitting down at the table with a pot of tea and _Éléments de géométrie algébrique_ Volume I and a stack of white printer paper.

Sibylla was saying: —that the names for mathematical objects in French are the essentially the same as the ones in English. Rings are anneaux and sheaves are faisceaux—

Cindy said: Well, yeah, what else would they be?

Sibylla said: But the fact that you take this for granted is itself remarkable. Of course in some sense it’s trivial that something you call a ring in English should be called un anneau in French, but in another sense it isn’t at all. If names for mathematical objects are chosen idiosyncratically based on a vague correspondence between the ordinary sense of the word and something about the highly abstract nature of the mathematical object, presumably here there’s some sort of circular structure, then there’s no reason why you couldn’t have chosen a _different_ word in French with its own idiosyncratic relationship to the mathematical object but your translators have chosen to gently preserve the metaphor across every language.

I poured myself some tea. Cindy said: Okay, I see what you’re saying.

Sibylla: So, presumably, English- and French- and German-speaking mathematicians everywhere begin with the same physical metaphor when studying rings or sheaves and so on, and it’s a charming thought but then one wonders to what extent mathematicians are constrained by their analogies and perhaps we’d be better off if we had a richer variety of physical things to point to. Suppose if rings were instead called, well, I can’t generate any plausible alternatives being unacquainted with the actual mathematical definition but you see the idea—

Cindy: Right, yeah, I’ve never thought of it that way. But, look, on the other hand, I'm pretty sure when Hilbert said Ring in German he meant it like an association of people, like an organized crime ring. I guess ‘group’ was already taken. But that’s not what people usually mean by ring anymore, so we’re basically stuck with these connotations of circularity like you said and of course it doesn’t help that one of the first examples of rings anyone learns about is the integers modulo n so people get stuck on this image of cycles and periodicity. I mean, really, now that you bring it up, we should just make up random syllables whenever we have to name some mathematical object—

Sibylla: Oh, but—

Cindy said, You haven’t studied algebra, right? Let me explain the sense in which— and she got out a piece of paper and started writing down the ring axioms and Sibylla leaned in to see. So, first, you have _closure_—

Dr. Wu entered with a list written on a scrap of paper and said: I have a lot of food to pick up. Does anyone want to help me carry it?

Cindy said Dad, we’re busy, so I went with him to downtown Flushing. We returned with a seemingly arbitrary and unrelated assortment of takeout: Beijing roast duck with scallions and crepes, cartons of wonton and tripe soup, stir-fried lotus root, a whole fish covered in chiles, thick boiled dumplings, steamed buns, a single container of chicken lo mein for Kevin. Cindy and Sibylla decamped to the sofa with their books and papers. Dr. Huang said: I do cook, but cooking on Thanksgiving isn’t worth it. We just order everyone’s favourites.

* * *

We sat down to eat. Dr. Wu said: So, Sibylla, what do you do for work? I think Ludo mentioned that you work in publishing?

I held my breath. Sibylla seemed to be in good spirits, though. She said: Almost certainly not in the way you’d think. I manually correct errors in articles that have been transcribed by a defective piece of OCR software.

Dr. Wu said: Oh, I know exactly what you mean. You should see what OCR software does to mathematical papers, it’s terrible. It’s almost funny when you think of all the effort that went into typesetting mathematical papers in the days before digital typesetting, and now we have so many problems trying to get them digitised. I think we all wish we could just beam mathematical ideas directly into our colleagues’ heads and bypass the paper-writing step.

Dr. Huang said: Oh, I don’t know. I do like a well-written paper, but they’re so rare.

I don’t know what I’d expected. So many of my earliest memories involved Sib typing and hating it that I’d expected the announcement of her job to create a bigger fuss, somehow, like Cindy’s parents would suddenly become scornful or pitying or condescending. The conversation moved on. Dr. Wu said that he once had to help with the typesetting for a Russian volume which had been a nightmare, and Dr. Huang said that she once traveled to Russia in the nineties for a conference and, lacking a common language to explain to the customs officer what she studied, had gotten out the undergraduate textbook she’d had with her and showed him the drawings of circles and dots being partitioned this way and that, and Sib became interested in this story and started asking a battery of questions. I started out closely watching Sib and listening to what she said, but I started to relax once I realised she didn’t seem terribly bored.

Cindy and Kevin had started having a low-volume argument between themselves on the other end of the table, but it didn’t seem too heated. Cindy looked up at me. I shrugged and smiled.

* * *

The next day Sibylla and I each paid $1 to enter the Metropolitan Museum of Art. We went to go see the quite decent Asian art section, but then the museum started getting crowded with Thanksgiving tourists and Sibylla deflated and said The entire Midwest seems to have arrived in this gallery. We left and got lunch at a halal cart, then headed to the Whitney which was considerably less crowded. Then I escorted her as far as the PATH stop and took the train back to Flushing.

When I returned, Cindy said: Do you mind if we leave tomorrow instead of Sunday? I have some work to do and I’d rather do it in my dorm.

It was dark by the time we boarded the bus the next day. The lights were dimmed. There was something strange about being on a bus at night, as though you were in a cocoon hurtling through space outside ordinary time.

Cindy said quietly, To be honest, I don’t really have much work I need to do. I just hadn’t realized how much I didn’t really want to be back there.

Yeah?

I mean, there’s nothing wrong, it just reminds me too much of when I was at home last year.

Makes sense.

Yeah, Cindy said. So, uh, anyway, that’s your mom.

I nodded.

Honestly, when you said she worked in publishing I sort of assumed she was an editor or something. Is her job really just fixing mistakes—

Yes.

Sorry, I didn’t mean to imply there was something wrong with that. But does she actually want to be doing this?

No, of course not.

Cindy asked whether Sib had finished her PhD & I said no, she dropped out a few months into her first year & Cindy asked when & I said 1985, and I could see her formulating the obvious question in her mind and trying to calculate backwards. I said: She didn’t drop out because of me. It was a few years before that.

Cindy said: So your mom’s not interested in academia? Couldn’t she be a lecturer, or an actual editor or something? I’m sure someone as smart as her could find _something_.

I looked out the window. There was nothing to see. Where could I even begin? There would never be a _Good Will Hunting_ ending for Sib where a professor or a therapist discovered her and set her on a path to self-actualisation. Life was not so simple. Everyone knew that the maths problems Will Hunting had solved while working as a janitor in the film weren’t actually as difficult as the film implied; Cayley had given the number of trees on n labeled vertices in the 19th century, and while it was nontrivial to enumerate homeomorphically irreducible trees in general, simply doing it for n=10 wasn’t hard. That was the problem with films about anyone trying to do anything difficult: If you wanted to have a character have a eureka moment that could be easily explained and that could neatly tie up the problem with a bow, you had to simplify the situation into something unrecognizable.

Grothendieck was surely worthy of a Hollywood film. He’d been born to anarchist parents and had escaped from a German internment camp intending to assassinate Hitler and now he was living in seclusion sending out thousand-page manuscripts to his colleagues. But you couldn’t make one. How would you even begin to explain what algebraic geometry was? How would you condense tens of thousands of pages of writing into a single blackboard? Maybe you could just show the sea rising until it covered the earth.

Perhaps Sibylla would be happy if she lived in seclusion somewhere in France where nobody could find her. Maybe she would write to me, or maybe she wouldn’t. I did not know how to begin explaining that it was not Sibylla contra the academic world or the non-academic world or her menial job, but the world itself, irreducible and unsurmountable.

I said: Have you ever seen Seven Samurai?

Cindy said: What? You mean the Japanese movie? Yeah, my brother likes it. What about it?

I did not know how to explain Seven Samurai and Yamamoto’s tapes and everything else. I said: My estimate is that Sibylla has watched Seven Samurai over two thousand times.

What? Are you serious? How is that even possible?

It’s her favourite film. She pops the video in the video player and presses play before she goes to bed most nights and has been doing this since before I was born.

Ludo, is your mom okay?

I did not know how to explain so I said nothing.

We sat in silence for a few minutes. Small towns passed by on the freeway. People would be checking into roadside motels now and checking out the following morning. Cindy said: Okay, sorry, you obviously don’t want to talk about this. I’ll leave you alone. I just didn’t realise it was like this. Your mom seemed nice and interesting when I talked to her, and she actually wanted to hear about math which _never_ happens, and I could tell she actually understood what I was telling her and wasn’t just humouring me, and you’re telling me that she spends all her time at home checking for typos in terribly OCR’ed magazine articles and watching the same movie 2,000 times. I mean—okay, sorry, I’ll stop. I just don’t get it.

I said: Well, that’s not fair, she also reads a lot of books.

Cindy was in the middle of pulling out her Walkman. It was too dark to read. She said: Ludo, if you don’t want to talk about it, just say so, but I don’t understand what you’re getting at or what you’re trying to do.

She put her headphones on before I could say anything else.

I dozed off again. When I woke up we were in the Chinatown in Boston and I felt heavy and exhausted. I took my backpack and Cindy and I took the Red Line back to Harvard in silence.

* * *

I arrived at my door and started rummaging through my backpack for my keys when I heard Thomas inside saying, Ludo, is that you? Wait a second—

There seemed to be a minor commotion inside. I yelled No, don’t worry about it, I’ll come back tomorrow! I remembered just then that I’d told Drew that I’d be back on Sunday, and I decided I’d best leave them alone.

I turned around and walked back out of the building. Sleeping outside seemed out of the question; the campus police hadn’t been happy the time I fell asleep on a bench outdoors, and besides the temperature was −5 degrees. I realized I could go to Cindy’s. Maybe if she didn’t want to talk to me, she’d still let me sleep on the couch in her suite.

The Yard was deserted. I couldn’t see too far in any direction through the flurries, and the snow dampened any sound. I felt like the only person in the world, an outcast and an exile. Nun ist die Welt so trübe, der Weg gehüllt in Schnee! Now the world is so desolate, the path covered in snow. I sang this to myself a few times, not remembering most of the rest of the words, feeling sorry for myself, but presently I ended up at Matthews before I knew it. It was only a minute’s walk.

I walked up the stairs and knocked on the door of Cindy’s suite. I heard her running toward the door. Who is it? She said.

It’s Ludo, I said.

She opened the door wearing pyjamas. I said, I’m really sorry to bother you, but I can’t sleep in my room tonight. Is there any way I could sleep on your couch? I’ll be so quiet you won’t even know I’m here and I’ll leave early tomorrow morning.

Why? What’s wrong with your room? Cindy said.

My roommate is using it, I said. Cindy frowned. And his boyfriend, I said.

Oh, I see, Cindy said. Okay, sure.

We went to her room. Her laptop displayed the Ultima Online pause screen. She said: You should probably just sleep here since I don’t want to surprise my roommates.

We set up her sleeping bag. I said: Sorry about—about the bus.

It’s fine.

I can explain if you still want to hear it.

Cindy looked at me and didn’t say anything. I put my head in my hands and exhaled. I was no closer to being able to explain. Maybe even a description would be a start. I said: Sibylla hasn’t tried to move or get a different job for—for my entire life, I suppose.

So what does she actually do when she’s not typing?

She’s not a total shut-in if that’s what you’re wondering. We go to the bookstore, we go to the library, we see movies and concerts, once we went hitchhiking in France. It’s just that those things are like—

Like what?

Like breaks or distractions.

From her job? I thought her job was part-time and she didn’t care that much about it.

No, from what life is for her in general.

What do you mean?

Sibylla tried to kill herself once. Now she can’t because she’s responsible for me, or at least she couldn’t for a while, but can’t doesn’t mean doesn’t want to.

Cindy had been fidgeting with her pen. Now she stopped. She stared at me.

I said, You know who Kenzo Yamamoto is, right?

Cindy frowned. Yeah.

You know that CD, the Bootleg Sessions or whatever it’s called?

Yeah, I didn’t really like it, the audio quality was terrible. What about it?

Kenzo Yamamoto and I recorded that for her.

Cindy put her pen down on her desk with more violence than strictly necessary. Ludo, what are you talking about? I mean, sorry, but you’re not making any sense.

I said: I was walking through London because I was at a loss for what to do and I walked by his house and heard him playing the piano. If you look at the liner notes you’ll see where it says Stephen ‘Ludovic’ Newman. I know it sounds surprising but it would be even more surprising if I’d just lied to you about something so easily falsifiable so you’ll have to believe me on this.

Cindy didn’t seem entirely placated. She said, I—well—okay. Most people would pull out that story at a party in their first week here, but I guess you wouldn’t. Wait, you couldn’t have been more than— You know what, never mind. Go on.

I said: The version on that CD is chopped up and completely worthless but someday I’ll play the real one for you, it’s 22 hours long, you’ll like it, I promise. We recorded it for Sib and I guess I’d been hoping she’d listen to it and—I don’t know, find a new job or find a new city to live in or become someone who wasn’t her. I was only 11, you’re right, so it’s not like I could think very rationally at the time.

I used to think that if Sibylla could always watch Seven Samurai then she’d always be beautiful. But of course if Seven Samurai could have saved her then it already would have. I said: Sibylla loved the recording, and I could tell because she didn’t watch Seven Samurai for an entire month. But she’s still sitting in the house doing her job which she hates and the only real difference is that she’s a few years closer to dying.

Cindy said: Ludo, wait, back up a little. Do you—you’re really saying that you think you’re keeping your mom from killing herself.

I said: Well obviously she’d never say that to me but that’s really a lie of omission more than anything.

Cindy said: How—what—

I said: Imagine two people, one of whom dies at time t and one of whom—

Cindy said: Oh, come on, Ludo, I can tell that you’re just going to make the obvious argument and you really don’t need a mathematical model for it, it’s not going to make your argument more precise.

I stayed silent. I’d expected Cindy to be unsettled, but I hadn’t expected her to be so shaken, even angry. She said: Why do you even think that’s true?

Why what’s true?

That you’re preventing her from killing herself.

I had to gather my thoughts for this one. I said: She felt life wasn’t worth living before I was conceived and nothing’s changed since then except that I’m here and she hasn’t tried again. I don’t know what other conclusion to draw from this except that she doesn’t want me to be without a source of financial support, though that’s no longer applicable, or that she would feel bad about making me upset if she died.

Cindy said: Why is the second reason bad?

I said: Well, you can’t just keep living to keep other people from being sad. It’s sentimental and unsound—

Cindy said: Well, why would you be upset if Sibylla died?

It wasn’t like I hadn’t considered it plenty of times before, or hadn’t idly planned for the eventuality while carefully sidestepping what it meant, but eventually I got used to sidestepping and now I wasn’t and the idea was so awful that I couldn’t speak for a while.

Cindy said, finally: If Sibylla feels that way about you and you’re still completely convinced she must not find life worth living then I don’t know what to tell you.

I’d been looking at a spot on the floor. When I looked up Cindy was silently crying. I’d never seen her cry before and I was certain it was not because of me and Sib. I thought about what she said about last year and how it had been the worst thing in the world and I got up and put a hand on her shoulder.

Cindy silently dabbed at her face with a tissue and blew her nose. Then she turned to me and said I’m fine.

Okay, I said.

I turned the electric kettle on and dug up some hot cocoa mix and walked around her tiny room in circles while the water heated up. Then I made us hot cocoa; we didn’t have marshmallows but hopefully we’d get by.

Thanks, she said when I handed her the mug.

We drank our cocoa in silence. When I was halfway done, Cindy said: Do you remember how you told me back in September that you needed to come to university to study math because it’s easy to learn new languages but hard to learn math?

Sure, I said. Maybe not in those exact terms.

Yeah, sure. Well, you know that’s bullshit, right? It doesn’t make any sense.

Why not?

Cindy looked down into her mug. She said, You know all those languages because Sibylla taught you even if she didn’t literally sit down with you and teach you every single word. It’s kind of obvious once you meet her.

* * *

I drank the rest of my cocoa. I figured, in for a penny, in for a pound, and I said: Do you know that part in Seven Samurai where Katsushiro hides behind the entryway and prepares to hit the incoming samurai with a stick as a test?

Cindy said: Well, I’ve never actually seen it. My brother always watched Japanese movies without subtitles since he said he was trying to learn Japanese, which, by the way, drove my mom crazy, so I figured there was no point in me trying to watch it.

She said: Anyway, why do you ask?

I told her about my biological father and about the others and finally about Red Devlin.

We fell asleep at around 5 a.m. At this time of year the sky was still pitch-black.

* * *

A week passed. We sat for the William Lowell Putnam Mathematical Competition. Afterwards Cindy said, Well, there’s absolutely no way I made Fellow, since I didn’t get A2 at all and I think my solution for B5 was probably wrong. Maybe I can just tell people I got drunk the night before.

Another week passed. I convinced Cindy to go to The Importance of Being Earnest with me on opening night, and when we entered the theatre I saw Drew in a row by himself waving at me, so we joined him.

I tittered along with everyone else when Jack said The fact is, Lady Bracknell, I said I had lost my parents. It would be nearer the truth to say that my parents seem to have lost me. At the interval we reentered the bright foyer and people excitedly said Wow that wasn’t what I was expecting This is a lot funnier than I expected Yeah I should see more old plays Yeah Oscar Wilde is really funny That guy is in my freshman seminar but I didn’t know he did theatre Which guy? The guy playing the guy in the brown suit and I sat down on a bench and put my head in my hands.

Cindy sat down next to me. Are you okay?

Yeah.

What’s going on?

Nothing.

Ludo, come on, seriously. Do you want to leave?

No, it’s fine, I want to see the last act. I’ll tell you afterward.

We went back in. I laughed along with everyone when Lady Bracknell said A _handbag_? and Cindy gasped when Jack produced the handbag. Thomas was quite good as Jack. He might been overacting a bit, but it was probably just opening-night nerves.

Afterward, Thomas reemerged, still in his stage makeup, and we congratulated him and Drew hugged him and said You were amazing! and quickly kissed him in front of everyone. Thomas invited us to the cast party, but I said I was too tired, and Cindy and I left.

It was snowing but not too cold. We went to the Science Center, nearly empty this time of night, and took the stairs to the rooftop. We sat in our usual spot where passersby couldn’t see us since Cindy didn’t want to get in trouble. I told her that the last time I’d seen the play in any form was with Red Devlin, and I hadn’t been able to watch it since.

Cindy said she was sorry, and I said I was too.

We sat in silence for a while, watching the snow fall. Then Cindy said: Sorry, I know this is beside the point, but did you see that George Sorabji is coming here for a book signing next semester?

Ugh, I didn’t, I said. Thanks for the warning.

Cindy: I always felt like George Sorabji was some kind of fraud or impostor or something, and I don’t mean his physics research, I’m sure all that is fine. I mean, I can’t even put my finger on anything specific, but there was just something _off_ about him and now I feel vindicated.

I: Do you remember how he’d say things like, if walls didn’t have electrical charge then you could walk through them? But of course—

Cindy: Right, clearly without electrical charge there wouldn’t be walls. I mean, clearly he must know this—

I: Right, but it’s just such a pointless—

Cindy: Yeah, I always imagined him as the sort of guy where if you pointed something out like that to him he’d smile condescendingly at you and say Well, aren’t you a smart child, but you see, I’m trying to appeal to a general audience.

I: I didn’t even mention how he told me that being a scientist was really about trying to communicate to people who were utterly resistant to anything mathematical and challenging and really only wanted a naive sense of scientific wonder.

Cindy: Of COURSE he’d say that. Every time you say something about him it just gets worse. I felt patronised watching that show and it had nothing to do with him talking to a general audience. It’s not like I know any physics. It’s just—he doesn’t give a shit about whether people actually learn any math or science, he just wants them to legalise marijuana or whatever. Maybe people wouldn’t be so resistant to anything challenging if he didn’t talk to them like they were 4 years old.

I: Right.

Cindy: Right. So, uh, sorry again for getting off-topic.

I: No, it’s fine, you didn’t.

* * *

The Putnam results were released. Cindy made Fellow along with someone else in my math class, and Harvard beat MIT this year and placed first. I got an Honorable Mention.

Of course we had a department social to celebrate, and I dragged Cindy to it. She gritted her teeth during the applause and briefly congratulated the other Fellow and left. I stayed for more mingling and cake.


	3. THIS is Seven Samurai?

Finals, then Winter Break. The AMS sent me $250 in Putnam prize money. Drew got an A− in calculus. Sibylla, apropos of nothing, started a blog.

I wasn’t going anywhere. Cindy was travelling to Houston to see her grandparents, but she hadn’t wanted to go to New York before then. The two of us were left to fend for ourselves on the nearly empty campus. We bought a hot plate from a late-graduating senior and cooked a lot of frozen dumplings. Cindy’s suite had a TV and a VCR player, so one day I got Seven Samurai from the Blockbuster.

Cindy said: It’s three and a half hours long? Are you serious? She asked if she could read a book during the boring parts and I said technically yes but it didn’t matter since there weren’t any boring parts. I pressed play.

I hadn’t watched the film in months, but I still focused on Cindy’s reactions. She spent a lot of time frowning as though in deep concentration. I’d expected her to laugh when Mifune fell off the horse but she only frowned harder. Gradually she seemed to warm to it, and I could tell she was captivated by Mifune’s speech at the end of Part One, when he indicted the samurai and in doing so revealed himself to be an orphaned farmer’s son. At the intermission, I lowered the volume on the music and said casually: So, what did you think?

Cindy said: You didn’t tell me this was an ACTION MOVIE with COMEDY and ROMANCE. The way you described it to me made it sound like it was going to be abstract and symbolic and all about being on a mental quest to achieve enlightenment or something and there were going to be all these serious scenes where the samurai get tested and initiated, and I figured if your MOM liked it then it must be artistic and really hard to understand. I spent the first half hour trying to figure out what the movie MEANT. THIS is Seven Samurai?

I had not expected this reaction. I said: Yeah, this is Seven Samurai. Do you like it?

Cindy said: Yeah, it’s pretty good so far.

The intermission ended. Cindy was riveted when Mifune wept upon seeing the orphaned baby placed in his arms. _This baby is me!_ She became indignant when Shino’s father started beating her because she’d slept with Katsushiro. She said: Why don’t they just get married? I said it was because he was a samurai and I’d explain to her afterward. Sibylla had been very knowledgeable about social classes during the Sengoku period. She hadn’t really been interested in any other aspects of the Katsushiro-Shino relationship.

Cindy was silent as the credits started. As I did occasionally, I found myself wishing I could erase all my memories of Seven Samurai and see it again for the first time. Seeing someone else see Seven Samurai for the first time was likely the closest I’d ever get. Finally, Cindy turned to me and said: Hmmm, that was—I’m not even sure what to say. That was a good movie.

I nodded. We cooked more dumplings and I explained why Katsushiro would never be able to marry a farmer’s daughter. Okay, sure, but it’s still sad. Yes, it is.

* * *

I asked Sib whether she’d be willing to loan me Yamamoto’s tapes and she assented. They’d probably take a week to arrive by mail. I thought I could play them in my dorm room and invite everyone: Cindy, Drew & Thomas, last semester’s Tonal Music section, maybe my Math 55 classmate who’d placed third in the Cliburn Junior Competition. A salon evening! There was nothing in the world like hearing the B-flat major prelude transposed to G major for the first time when you’d been expecting to hear the C major fugue. Mozart for Study and Relaxation this was not (though I hoped that Drew might enjoy hearing it anyway).

The issue was that the tapes were 22 hours long, and you really couldn’t just play an excerpt. It would likely have to be multiple evenings; I would likely have to provide refreshments. Fortunately I had the rest of the holiday to work something out.

**Author's Note:**

> More content notes: There's some recurring discussion of Sibylla's depression and suicidal ideation, as well as briefer mentions of the same for an OC, and a reference to the death that occurs toward the end of the novel. All of the above is at a canon-typical level. There are some references to off-screen homophobia (completely unrelated to the items listed previously).
> 
> Thank you to everyone who did beta-reading for this fic: A, M, and Gammarad. All remaining errors are, of course, my own.


End file.
